00:01
Hello student the question say the acceleration of motorcycle is given by a equal to 1 .5 t minus 0 .10 t square and the motorcycle is at rest at the origin at time t equal to 0 we want to find its position as a function of time and second its maximum velocity.
00:21
So first we write here given data given data acceleration is given as a function of time a equal to 1 .5 .4.
00:33
T minus 0 .10 t square and at t equal to zero at t equal to zero particle is at origin so we can say x equal to zero and its velocity is also zero means v equal to zero first we want to find the position as a function of time so first we integrate this equation a equal to 1 .5 t minus 0 .10 t square if we integrate this equation we find the velocity as a function of time t so we can say v equal to 1 .5 integration of t is t square upon 2 minus 0 .10 into t cube upon 3 so we can say plus c is also there so v equal to 1 .5 t squared upon 2 minus 0 .10 upon 3 t cube plus c so here given is as t equal to 0 at t equal to 0 our v is 0 so put these two value in equation number 1 so 0 equal to 1 .5 by 2 into 0 minus 0 0 0 upon 3 into 0 plus c so from this one we can say c equal to 0 this c equal to 0 put in equation number 1 so we can say v equal to v equal to 1 .5 t square upon 2 minus 0 .10 upon 3 t cube is the equation of velocity as a function of time at equation number 2.
02:33
Now, if we integrate again the equation of velocity, we got position.
02:41
So again integrating, again integrating.
02:52
So, x equal to, if we integrate again, 1 .5 upon 2 is constant.
02:59
Integration of t square is t a cube upon 3 minus 0 .10.
03:05
Upon 3 into t 4 upon 4 plus c so again at t equal to 0 t equal to 0 x is 0 so x equal to 0 put these to value we can say 0 equal to 0 minus 0 plus c so c equal to 0 if we put this c equal to 0 in this equation we got value at position as a function of time so we can say x t equal to 1 .5 upon 6 t q minus 0 .10 upon 3 into t 4 upon 4 if is only this further we can say x t in position as a function of time equal to 0 .75 5 .3 t cube minus 0 .10 upon 12 t 4 so this is our first answer position as a function of time...